Figure 20 - 1 Moriah's Candle Company manufactures candles. The company buys wax in 45-Kilogram containers that cost $17 each. The company uses 25,000 containers per year, and usage occurs evenly throughout the year. The average cost to carry a 45-Kilogram container in inventory per year is $3, and the cost to place an order is $9. The company works 250 days per year.
Refer to Figure 20-1. The economic order quantity (rounded) is

Question

Quizplus · Accepted Answer

Using the formula for economic order quantity (EOQ):

EOQ = sqrt((2DS)/H)

where 
D = annual demand (number of units)
S = setup or ordering cost per order
H = holding cost per unit per year

Given:
D = 25,000 containers per year
S = $9
H = $3

First, we need to determine the total annual cost (TAC) of ordering and holding inventory at the EOQ:

TAC = DS/Q + HQ/2

where Q = EOQ

TAC = (25,000 x 9) / 387 + (3 x 387) / 2
TAC = 2,300.97

To find the EOQ, we set the derivative of the TAC equation with respect to Q to zero:

d(TAC)/dQ = (-DS/Q^2) + (H/2) = 0

Solving for Q, we get:

Q = sqrt((2DS) / H)
Q = sqrt((2 x 25,000 x 9) / 3)
Q = 387.3

Rounding to the nearest whole number, the EOQ is 387 containers. Therefore, the best choice is D.

Figure 20 - 1 Moriah's Candle Company Manufactures Candles